Data update
This commit is contained in:
Ingy döt Net
parent
29a5eea0d4
commit
5c1bb7bfa9
2011 changed files with 35081 additions and 3229 deletions
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#include <algorithm>
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#include <cstdint>
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#include <iomanip>
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#include <iostream>
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#include <map>
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#include <set>
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#include <sstream>
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#include <string>
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#include <vector>
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// A point of the current Catmull-Clark surface.
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class Point {
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public:
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Point() : x(0.0), y(0.0), z(0.0) { }
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Point(const double& aX, const double& aY, const double& aZ) : x(aX), y(aY), z(aZ) { }
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Point add(const Point& other) const {
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return Point(x + other.x, y + other.y, z + other.z);
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}
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Point multiply(const double& factor) const {
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return Point(x * factor, y * factor, z * factor);
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}
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Point divide(const double& factor) const {
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return multiply(1.0 / factor);
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}
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bool operator<(const Point& other) const {
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return ( x < other.x ) || ( ( x == other.x && y < other.y ) )
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|| ( x == other.x && y == other.y && z < other.z );
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}
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bool operator==(const Point& other) const {
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return x == other.x && y == other.y && z == other.z;
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}
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Point& operator=(const Point& other) {
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if ( *this != other ) {
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x = other.x; y = other.y; z = other.z;
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}
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return *this;
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}
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std::string to_string() const {
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return "(" + format(x) + ", " + format(y) + ", " + format(z) + ")";
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}
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private:
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std::string format(const double& value) const {
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std::stringstream stream;
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stream << std::fixed << std::setprecision(3) << value;
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return ( value >= 0 ) ? " " + stream.str() : stream.str();
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}
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double x, y, z;
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};
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// Return the centroid point of the given vector of points.
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Point centroid(const std::vector<Point>& points) {
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Point sum;
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for ( const Point& point : points ) {
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sum = sum.add(point);
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}
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return sum.divide(points.size());
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}
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// An edge of the current Catmull-Clark surface.
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class Edge {
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public:
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Edge(Point aBegin, Point aEnd) {
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if ( aEnd < aBegin ) {
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std::swap(aBegin, aEnd);
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}
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begin = aBegin; end = aEnd;
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mid_edge = centroid({ begin, end });
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hole_edge = false;
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}
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bool contains(const Point& point) const {
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return point == begin || point == end;
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}
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bool operator<(const Edge other) const {
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return ( begin < other.begin ) || ( begin == other.begin && end < other.end );
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}
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bool operator==(const Edge& other) const {
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return contains(other.begin) && contains(other.end);
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}
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bool hole_edge;
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Point begin, end, mid_edge, edge_point;
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};
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// A face of the current Catmull-Clark surface.
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class Face {
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public:
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Face(std::vector<Point> aVertices) {
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vertices = aVertices;
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face_point = centroid(vertices);
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for ( uint64_t i = 0; i < vertices.size() - 1; ++i ) {
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edges.emplace_back(Edge(vertices[i], vertices[i + 1]));
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}
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edges.emplace_back(Edge(vertices.back(), vertices.front()));
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}
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bool contains(const Point& vertex) const {
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return std::find(vertices.begin(), vertices.end(), vertex) != vertices.end();
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}
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bool contains(Edge edge) const {
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return contains(edge.begin) && contains(edge.end);
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}
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std::string toString() const {
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std::string result = "Face: ";
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for ( uint64_t i = 0; i < vertices.size() - 1; ++i ) {
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result += vertices[i].to_string() + ", ";
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}
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return result + vertices.back().to_string();
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}
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std::vector<Point> vertices;
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std::vector<Edge> edges;
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Point face_point;
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};
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// Return a map containing, for each vertex,
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// the new vertex created by the current iteration of the Catmull-Clark surface subdivision algorithm.
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std::map<Point, Point> next_vertices(const std::vector<Edge>& edges, const std::vector<Face>& faces) {
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std::map<Point, Point> next_vertices = { };
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std::set<Point> vertices = { };
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for ( const Face& face : faces ) {
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for ( const Point& vertex : face.vertices ) {
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vertices.emplace(vertex);
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}
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}
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for ( const Point& vertex : vertices ) {
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std::vector<Face> faces_for_vertex = { };
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for ( const Face& face : faces ) {
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if ( face.contains(vertex) ) {
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faces_for_vertex.emplace_back(face);
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}
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}
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std::set<Edge> edges_for_vertex = { };
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for ( const Edge& edge : edges ) {
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if ( edge.contains(vertex) ) {
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edges_for_vertex.emplace(edge);
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}
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}
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if ( faces_for_vertex.size() != edges_for_vertex.size() ) {
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std::vector<Point> mid_edge_of_hole_edges = { };
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for ( const Edge& edge : edges_for_vertex ) {
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if ( edge.hole_edge ) {
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mid_edge_of_hole_edges.emplace_back(edge.mid_edge);
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}
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}
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mid_edge_of_hole_edges.emplace_back(vertex);
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next_vertices[vertex] = centroid(mid_edge_of_hole_edges);
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} else {
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const uint64_t face_count = faces_for_vertex.size();
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const double multiple_1 = static_cast<double>(( face_count - 3 ) / face_count);
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const double multiple_2 = 1.0 / face_count;
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const double multiple_3 = 2.0 / face_count;
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Point next_vertex_1 = vertex.multiply(multiple_1);
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std::vector<Point> face_points = { };
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for ( const Face& face : faces_for_vertex ) {
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face_points.emplace_back(face.face_point);
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}
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Point next_vertex_2 = centroid(face_points).multiply(multiple_2);
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std::vector<Point> mid_edges = { };
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for ( const Edge& edge : edges_for_vertex ) {
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mid_edges.emplace_back(edge.mid_edge);
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}
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Point next_vertex_3 = centroid(mid_edges).multiply(multiple_3);
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Point next_vertex_4 = next_vertex_1.add(next_vertex_2);
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next_vertices[vertex] = next_vertex_4.add(next_vertex_3);
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}
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}
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return next_vertices;
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}
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// The Catmull-Clarke surface subdivision algorithm.
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std::vector<Face> catmull_clark_surface_subdivision(std::vector<Face>& faces) {
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// Determine, for each edge, whether or not it is an edge of a hole, and set its edge point accordingly.
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for ( Face& face : faces ) {
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for ( Edge& edge : face.edges ) {
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std::vector<Point> face_points_for_edge = { };
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for ( const Face& search_face : faces ) {
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if ( search_face.contains(edge) ) {
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face_points_for_edge.emplace_back(search_face.face_point);
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}
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}
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if ( face_points_for_edge.size() == 2 ) {
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edge.hole_edge = false;
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edge.edge_point = centroid({ edge.mid_edge, centroid(face_points_for_edge) });
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} else {
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edge.hole_edge = true;
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edge.edge_point = edge.mid_edge;
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}
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}
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}
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std::vector<Edge> edges = { };
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for ( const Face& face : faces ) {
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for ( const Edge& edge : face.edges ) {
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edges.emplace_back(edge);
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}
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}
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std::map<Point, Point> next_vertex_map = next_vertices(edges, faces);
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std::vector<Face> next_faces = { };
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for ( Face face : faces ) { // The face may contain any number of points
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if ( face.vertices.size() >= 3 ) { // A face with 2 or fewer points does not contribute to the surface
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Point face_point = face.face_point;
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for ( uint64_t i = 0; i < face.vertices.size(); ++i ) {
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next_faces.emplace_back(Face({
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next_vertex_map[face.vertices[i]],
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face.edges[i].edge_point,
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face_point,
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face.edges[( i - 1 + face.vertices.size() ) % face.vertices.size()].edge_point}));
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}
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}
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}
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return next_faces;
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}
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// Display the current Catmull-Clark surface on the console.
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void displaySurface(const std::vector<Face> faces) {
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std::cout << "Surface {" << std::endl;
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for ( const Face& face : faces ) {
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std::cout << face.toString() << std::endl;
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}
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std::cout << "}" << std::endl << std::endl;
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}
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int main() {
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std::vector<Face> faces = {
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Face({ Point(-1.0, 1.0, 1.0), Point(-1.0, -1.0, 1.0), Point( 1.0, -1.0, 1.0), Point( 1.0, 1.0, 1.0) }),
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Face({ Point( 1.0, 1.0, 1.0), Point( 1.0, -1.0, 1.0), Point( 1.0, -1.0, -1.0), Point( 1.0, 1.0, -1.0) }),
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Face({ Point( 1.0, 1.0, -1.0), Point( 1.0, -1.0, -1.0), Point(-1.0, -1.0, -1.0), Point(-1.0, 1.0, -1.0) }),
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Face({ Point(-1.0, 1.0, -1.0), Point(-1.0, 1.0, 1.0), Point( 1.0, 1.0, 1.0), Point( 1.0, 1.0, -1.0) }),
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Face({ Point(-1.0, 1.0, -1.0), Point(-1.0, -1.0, -1.0), Point(-1.0, -1.0, 1.0), Point(-1.0, 1.0, 1.0) }),
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Face({ Point(-1.0, -1.0, -1.0), Point(-1.0, -1.0, 1.0), Point( 1.0, -1.0, 1.0), Point( 1.0, -1.0, -1.0) })};
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displaySurface(faces);
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const uint32_t iterations = 1;
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for ( uint32_t i = 0; i < iterations; ++i ) {
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faces = catmull_clark_surface_subdivision(faces);
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}
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displaySurface(faces);
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}
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@ -0,0 +1,257 @@
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import java.util.ArrayList;
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import java.util.HashMap;
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import java.util.List;
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import java.util.Map;
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import java.util.Objects;
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import java.util.function.Function;
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import java.util.stream.Collectors;
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public final class CatmullClarkSurfaceSubdivision {
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public static void main(String[] args) {
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List<Face> faces = List.of( new Face(List.of( new Point(-1.0, 1.0, 1.0),
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new Point(-1.0, -1.0, 1.0),
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new Point( 1.0, -1.0, 1.0),
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new Point( 1.0, 1.0, 1.0) )),
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new Face(List.of( new Point( 1.0, 1.0, 1.0),
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new Point( 1.0, -1.0, 1.0),
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new Point( 1.0, -1.0, -1.0),
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new Point( 1.0, 1.0, -1.0) )),
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new Face(List.of( new Point( 1.0, 1.0, -1.0),
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new Point( 1.0, -1.0, -1.0),
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new Point(-1.0, -1.0, -1.0),
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new Point(-1.0, 1.0, -1.0) )),
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new Face(List.of( new Point(-1.0, 1.0, -1.0),
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new Point(-1.0, 1.0, 1.0),
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new Point( 1.0, 1.0, 1.0),
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new Point( 1.0, 1.0, -1.0) )),
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new Face(List.of( new Point(-1.0, 1.0, -1.0),
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new Point(-1.0, -1.0, -1.0),
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new Point(-1.0, -1.0, 1.0),
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new Point(-1.0, 1.0, 1.0) )),
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new Face(List.of( new Point(-1.0, -1.0, -1.0),
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new Point(-1.0, -1.0, 1.0),
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new Point( 1.0, -1.0, 1.0),
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new Point( 1.0, -1.0, -1.0) )) );
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displaySurface(faces);
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final int iterations = 1;
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for ( int i = 0; i < iterations; i++ ) {
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faces = catmullClarkSurfaceSubdivision(faces);
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}
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displaySurface(faces);
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}
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// The Catmull-Clarke surface subdivision algorithm.
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private static List<Face> catmullClarkSurfaceSubdivision(List<Face> faces) {
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// Determine, for each edge, whether or not it is an edge of a hole, and set its edge point accordingly.
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List<Edge> edges = faces.stream().map( face -> face.edges.stream() ).flatMap(Function.identity()).toList();
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for ( Edge edge : edges ) {
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List<Point> facePointsForEdge =
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faces.stream().filter( face -> face.contains(edge) ).map( face -> face.facePoint ).toList();
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if ( facePointsForEdge.size() == 2 ) {
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edge.holeEdge = false;
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edge.edgePoint = centroid(List.of( edge.midEdge, centroid(facePointsForEdge) ));
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} else {
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edge.holeEdge = true;
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edge.edgePoint = edge.midEdge;
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}
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}
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Map<Point, Point> nextVertices = nextVertices(edges, faces);
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List<Face> nextFaces = new ArrayList<Face>();
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for ( Face face : faces ) { // The face may contain any number of points
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if ( face.vertices.size() >= 3 ) { // A face with 2 or fewer points does not contribute to the surface
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Point facePoint = face.facePoint;
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for ( int i = 0; i < face.vertices.size(); i++ ) {
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nextFaces.addLast( new Face(List.of(
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nextVertices.get(face.vertices.get(i)),
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face.edges.get(i).edgePoint,
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facePoint,
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face.edges.get(Math.floorMod(i - 1, face.vertices.size())).edgePoint )) );
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}
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}
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}
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return nextFaces;
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}
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// Return a map containing, for each vertex,
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// the new vertex created by the current iteration of the Catmull-Clark surface subdivision algorithm.
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private static Map<Point, Point> nextVertices(List<Edge> edges, List<Face> faces) {
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Map<Point, Point> nextVertices = new HashMap<Point, Point>();
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List<Point> vertices =
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faces.stream().map( face -> face.vertices.stream() ).flatMap(Function.identity()).distinct().toList();
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for ( Point vertex : vertices ) {
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List<Face> facesForVertex = faces.stream().filter( face -> face.contains(vertex) ).toList();
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List<Edge> edgesForVertex = edges.stream().filter( edge -> edge.contains(vertex) ).distinct().toList();
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if ( facesForVertex.size() != edgesForVertex.size() ) {
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List<Point> midEdgeOfHoleEdges = edgesForVertex.stream().filter( edge -> edge.holeEdge )
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.map( edge -> edge.midEdge ).collect(Collectors.toList());
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midEdgeOfHoleEdges.add(vertex);
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nextVertices.put(vertex, centroid(midEdgeOfHoleEdges));
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} else {
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final int faceCount = facesForVertex.size();
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final double multipleOne = (double) ( faceCount - 3 ) / faceCount;
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final double multipleTwo = 1.0 / faceCount;
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final double multipleThree = 2.0 / faceCount;
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Point nextVertexOne = vertex.multiply(multipleOne);
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List<Point> facePoints = facesForVertex.stream().map( face -> face.facePoint ).toList();
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Point nextVertexTwo = centroid(facePoints).multiply(multipleTwo);
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List<Point> midEdges = edgesForVertex.stream().map( edge -> edge.midEdge ).toList();
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Point nextVertexThree = centroid(midEdges).multiply(multipleThree);
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Point nextVertexFour = nextVertexOne.add(nextVertexTwo);
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nextVertices.put(vertex, nextVertexFour.add(nextVertexThree));
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}
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}
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return nextVertices;
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}
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// Return the centroid point of the given list of points.
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private static Point centroid(List<Point> points) {
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return points.stream().reduce(Point.ZERO, (left, right) -> left.add(right) ).divide(points.size());
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}
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// Display the current Catmull-Clark surface on the console.
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private static void displaySurface(List<Face> faces) {
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System.out.println("Surface {");
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faces.stream().forEach(System.out::println);
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System.out.println("}" + System.lineSeparator());
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}
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// A point of the current Catmull-Clark surface.
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private static final class Point implements Comparable<Point> {
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public Point(double aX, double aY, double aZ) {
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x = aX; y = aY; z = aZ;
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}
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@Override
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public int compareTo(Point other) {
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if ( x == other.x ) {
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if ( y == other.y ) {
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return Double.compare(z, other.z);
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}
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return Double.compare(y, other.y);
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}
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return Double.compare(x, other.x);
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}
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@Override
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public boolean equals(Object other) {
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return switch ( other ) {
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case Point point -> x == point.x && y == point.y && z == point.z;
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default -> false;
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};
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}
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@Override
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public int hashCode() {
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return Objects.hash(x, y, z);
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}
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public Point add(Point other) {
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return new Point(x + other.x, y + other.y, z + other.z);
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}
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public Point multiply(double factor) {
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return new Point(x * factor, y * factor, z * factor);
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}
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public Point divide(double factor) {
|
||||
return multiply(1.0 / factor);
|
||||
}
|
||||
|
||||
public String toString() {
|
||||
return "(" + format(x) + ", " + format(y) + ", " + format(z) + ")";
|
||||
}
|
||||
|
||||
public static Point ZERO = new Point(0.0, 0.0, 0.0);
|
||||
|
||||
private String format(double value) {
|
||||
return ( value >= 0 ) ? String.format(" %.3f", value) : String.format("%.3f", value);
|
||||
}
|
||||
|
||||
private final double x, y, z;
|
||||
|
||||
}
|
||||
|
||||
// An edge of the current Catmull-Clark surface.
|
||||
private static final class Edge {
|
||||
|
||||
public Edge(Point aBegin, Point aEnd) {
|
||||
if ( aBegin.compareTo(aEnd) <= 0 ) {
|
||||
begin = aBegin; end = aEnd;
|
||||
} else {
|
||||
begin = aEnd; end = aBegin;
|
||||
}
|
||||
|
||||
midEdge = centroid(List.of( begin, end ));
|
||||
}
|
||||
|
||||
@Override
|
||||
public boolean equals(Object other) {
|
||||
return switch ( other ) {
|
||||
case Edge edge -> begin.equals(edge.begin) && end.equals(edge.end);
|
||||
default -> false;
|
||||
};
|
||||
}
|
||||
|
||||
@Override
|
||||
public int hashCode() {
|
||||
return Objects.hash(begin, end);
|
||||
}
|
||||
|
||||
public boolean contains(Point point) {
|
||||
return point.equals(begin) || point.equals(end);
|
||||
}
|
||||
|
||||
public boolean holeEdge;
|
||||
public Point edgePoint;
|
||||
|
||||
public final Point begin, end, midEdge;
|
||||
|
||||
}
|
||||
|
||||
// A face of the current Catmull-Clark surface.
|
||||
private static final class Face {
|
||||
|
||||
public Face(List<Point> aVertices) {
|
||||
vertices = new ArrayList<Point>(aVertices);
|
||||
facePoint = centroid(vertices);
|
||||
|
||||
edges = new ArrayList<Edge>();
|
||||
for ( int i = 0; i < vertices.size() - 1; i++ ) {
|
||||
edges.addLast( new Edge(vertices.get(i), vertices.get(i + 1)) );
|
||||
}
|
||||
edges.addLast( new Edge(vertices.getLast(), vertices.getFirst()) );;
|
||||
}
|
||||
|
||||
public boolean contains(Point vertex) {
|
||||
return vertices.contains(vertex);
|
||||
}
|
||||
|
||||
public boolean contains(Edge edge) {
|
||||
return contains(edge.begin) && contains(edge.end);
|
||||
}
|
||||
|
||||
public String toString() {
|
||||
return "Face: " + vertices.stream().map( point -> point.toString() ).collect(Collectors.joining("; "));
|
||||
}
|
||||
|
||||
public final List<Point> vertices;
|
||||
public final Point facePoint;
|
||||
public final List<Edge> edges;
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue